1. Field of the Invention
The present invention relates to a piezoelectric resonator or filter and a method for fabricating the same.
2. Description of Prior Art
A piezoelectric resonator is used mainly as an oscillator or as a clock element in computers, various apparatuses with a microprocessor, and other various digital apparatuses. A piezoelectric resonator comprises a piezoelectric plate cut from a single crystal such as quartz or a piezoelectric ceramic and driving electrodes formed appropriately on the plate. The resonator uses strong resonance generated by applying a driving voltage to the driving electrodes at a frequency around the resonance frequency determined by the sound velocity and the size of the piezoelectric plate. The piezoelectric resonators are used widely because they have superior properties though they have a simple structure.
The resonator traps vibration energy below the driving electrodes, while it is fixed at portions outside the driving electrodes. Then, it can be mounted in a package or on a print circuit board without effecting vibrations. This type of resonators is called as energy trapping type resonator.
Recently, various information apparatuses such as a personal computer perform high speed processing. Then, it is demanded to increase clock frequency for information apparatuses and peripherals thereof such as hard disk drives and CD-ROM drives. For a frequency range from ten to a few tens of MHz used in these apparatuses, resonators use thickness vibration such as thickness shear vibration, thickness twist vibration or thickness-extensional vibration having vibration frequency in reverse proportion to the thickness of the piezoelectric material. As the frequency becomes higher, the piezoelectric material becomes thinner. For example, the thickness is 100 .mu.m for frequencies exceeding 40 MHz. Then, various problems occur such as decrease in relative precision on forming, decrease in mechanical strength and increase in cost.
It is suggested in Japanese Patent laid open Publication 63-311808/1988 to form layers of lithium niobate with a reversed polarization in order make the thickness of the piezoelectric material for a particular frequency twice the counterpart in a previous resonator in correspondence to the frequency.
FIGS. 1A-1D show side views for illustrating processes for forming layers 102, 109 with a reversed polarization. A piezoelectric resonator 101 has driving electrodes 103 and 104 formed on opposing principal planes (top and bottom plane such as Z plane) 102a, 102b of a piezoelectric plate 102 cut from a lithium niobate single crystal.
In FIG. 1A, a wafer 105 is sliced from a lithium niobate single crystal subjected to poling, or the wafer 105 is sliced in a direction oblique by an appropriate angle relative to a polarization direction generated by the poling. A thin film 106 of titanium (Ti) is deposited on a plane of +c axis (or the top plane or +Z' plane in FIG. 1A) if the direction of the spontaneous polarization P.sub.S is in the direction of an arrow shown in FIG. 1A such as an upward direction.
Next, it is heated at a temperature between Curie temperature (about 1250.degree. C.) of lithium niobate and 1100.degree. C. to diffuse titanium in the titanium thin film 106 into the wafer 105, and a domain 109 with a reversed polarization is formed, as shown enlarged in FIG. 1B.
If the depth of the domain 109 with the reversed polarization is denoted as "t", surface charges generated in the wafer 105 under diffusion have a balanced state when the depth "t" is equal to a half of the thickness T.sub.3 of the wafer 105. Then, the depth "t" of the domain 109 with the reversed polarization extending from the top plane stops to increase further at about a half of the thickness T.sub.3 of the wafer 107, and the direction of the polarization P.sub.S ' of the domain 109 becomes reverse to that of the polarization P.sub.S. Next, as shown in FIG. 1C, a plurality of driving electrodes 103 and 104 are formed with patterning on the top and bottom planes of the wafer 107. Then, the wafer 107 is cut along dash and dot lines shown in FIG. 1C so that each element has the opposing electrodes 103 and 104. Thus, a piezoelectric resonator 101 shown in FIG. 1D is completed.
The piezoelectric plate 102 having the polarization P.sub.S and the reverse polarization P.sub.S ' has a thickness about twice that of a prior art single domain piezoelectric resonator for the same frequency. For example, if the thickness of the prior art piezoelectric resonator is about 150 .mu.m for vibration frequency of 26 MHz, that of the plate having the layers with a reversed polarization is about 300 .mu.m. This is ascribed that half wavelength resonance is excited in the former while one wavelength resonance is excited for the latter.
For a resonator using lithium tantalate, as described for example in Japanese Patent 1-158811/1989, a proton exchange layer is formed for reversed polarization, and a part of the polarization is reversed selectively. The resonator also intends to enhance the upper limit of frequency twice, similarly to the above-mentioned lithium niobate resonator. FIG. 2A shows a piezoelectric plate 112 cut from a 0.+-.10.degree. rotation X plate of lithium tantalate single crystal which has a polarization P.sub.S directed from one principal plane (+X' plane) 112a to another principal plane (-X' plane) 112b. Then, as shown in FIG. 2B, a polyimide layer (mask) 113 of thickness of about 5 .mu.m is applied to the +X' plane 112a by using for example spin coating. Then, as shown in FIG. 2C, it is immersed in a liquid for proton exchange processing heated at 250.degree. for about one hour. Then, a proton exchange layer 115 is formed extending from the -X' layer 112b. Then, the piezoelectric plate 112 removed from the liquid 114 and cleaned is heated at a high temperature, for example between 560 and 610.degree. C., below the Curie temperature of 620.degree. C. of the lithium tantalate, for an appropriate time. Then, as shown in FIG. 2D, a layer 112c with a reversed polarization having spontaneous polarization P.sub.S ' with a direction reverse to the polarization P.sub.S is formed from the -X' plane 112b to a half of the depth of the piezoelectric plate 112. Then, as shown in FIG. 2E, driving electrodes 116 and 117 are formed on the opposing principal planes (+X' and -X' planes) 112a and 112b. Thus, a piezoelectric resonator 111 is completed.
It is a problem for a resonator made of lithium niobate or lithium tantalate having a high Q and a large electro-mechanical coupling coefficient that spurious mode is liable to occur due to unnecessary vibration modes. Then, in order to excite a pure vibration mode, a resonator is fabricated by selecting a cut angle which forces thickness-extensional vibrations having principal displacement in the thickness direction and thickness shear vibrations having principal displacement parallel to the plate.
A thickness-extensional mode resonator couples weakly with other vibration modes. Then, by using this property, a resonator having small spuriouses inherently can be provided. When an optimum cut angle is selected for lithium niobate and lithium tantalate, the electromechanical coupling coefficient of thickness shear vibration mode is zero and only the thickness-extensional mode is excited. However, energy of first order wave (fundamental wave) is not trapped between the electrodes at the cut angle, and the resonator uses resonance of third order harmonic wave (third overtone) This is ascribed to the Poisson ratio of the lithium niobate or lithium tantalate being equal to or less than a third, and the first order resonance energy in the thickness-extensional mode cannot be trapped.
In the resonator using third order resonance, vibrations around the fundamental wave or the first order resonance are recognized as unnecessary vibrations or spuriouses. Therefore, if they are not suppressed sufficiently, vibrations of the fundamental wave are excited. Further, the third order resonance has worse properties than the first order resonance. On the other hand, there is a cut angle which excites not thickness-extensional mode, but only thickness shear mode.
A feature of the thickness shear mode different from the thickness-extensional mode is that two thickness shear vibrations perpendicular to each other exist at the same time in a plate excited with the thickness shear mode. Therefore, a resonator using the thickness shear mode has to contrive more to suppress spuriouses than that using the thickness-extensional mode.
A resonator using the thickness shear vibrations uses one of them as a main mode, and the other is recognized as unnecessary waves (spuriouses). Usually, an X-cut lithium tantalate uses a mode having faster sound velocity and a larger coupling coefficient as the main mode.
In order to suppress unnecessary waves due to width-extensional and length-extensional vibrations, it is also proposed that an element has a square size with sufficient room with respect to vibration space to damp spurious resonances with a sound absorbing material. However, if the absorbing material extends into the vibration space, the vibration characteristic is worsened remarkably. Then, this technique is not suitable for a small size element. On the other hand, Japanese Patent laid open Publication 5-160659/1993 proposes to provide an amorphous layer or an insulating layer at a side of an electrode. However, for a square element, the above-mentioned unnecessary waves having slow sound velocity are excited to a level about the same as the main waves. This situation is also observed similarly for a circular element.
In order to suppress the level of unnecessary waves having the slower sound velocity, it is also proposed to provide a rectangular element longer along the displacement direction of main vibrations. For an X-cut lithium tantalate plate having good temperature characteristics, the displacement direction of thickness shear vibration having a faster sound velocity (main vibration) is -53.degree. (Nihon Denpa Kogyo Giho, No. 6, November, 1979). The displacement direction is denoted as an angle .theta. relative to the Y axis in FIG. 3A.
A strip resonator is proposed to provide a compact resonator having good performance. As shown in FIG. 3B, a strip resonator is a long parallelepiped having a rectangular section and has opposing electrodes 201 and 201' extending along the whole width. Thickness twist vibration mode propagating perpendicular to the displacement direction of the main vibration and thickness shear vibration having slower sound velocity are suppressed, and the resonator has high Q. In order to suppress spurious resonances in a strip resonator, it is preferable that the longitudinal direction of the strip piezoelectric resonator using X-cut lithium tantalate is generally parallel to the displacement direction of thickness shear vibration. For example, the most appropriate cut angle (.theta. relative to Y axis in FIG. 3A) is -50.+-.20 (refer to Japanese Patent laid open Publication 1-36724/1989) or -57.+-.0.5.degree. (refer to Japanese Patent laid open Publication 2-13007/1990). The above-mentioned error range of the cut angle is about a few degrees, and this range is allowable because it is ascribed to crystalline symmetry and characteristics are not affected largely. Further, in the strip resonator, an appropriate ratio W/H of width W to height H and an appropriate ratio l/H of length l to height H are determined so that spurious resonances due to width or length do not overlap the thickness shear vibration mode as main vibration.
In order for the piezoelectric resonator 101, 111 subjected to polarization reversal processing to satisfy properties such as resonance frequency, resonance resistance, dynamic range and the like required for a resonator, it is necessary that the thicknesses of the layers with a reversed polarization are equal precisely to each other, that is, that the thickness of the layer with polarization P.sub.S is equal precisely to that of the layer with polarization P.sub.S '. Further, the properties as a piezoelectric resonator are deteriorated if uniform layers of reversed polarization with no undulation are not formed in a wide range in the wafer 107, 112.
As mentioned above, in order to form layers with a reversed polarization, application of a titanium thin film or the like is needed. Therefore, there are various parameters such as thickness control, stress control and the like, and it is difficult to control the thickness of the layers with a reversed polarization precisely at the thickness of a half of the piezoelectric plate. Then, there are problems that properties such as resonance frequency, resonance resistance, dynamic range and the like required for a resonator become worse.
Further, because the processing temperature for forming the layers with a reversed polarization is as high as the Curie temperature, it is difficult to control the homogeneous temperature, and it is necessary to manage the environment in order to prevent isolation of lithium. It is also a problem that the plate is contaminated by the wall of the heating chamber, and this deteriorates the properties for a resonator.
Further, the preparation of the layers with a reversed polarization accompanies a change in composition such as a diffusion layer of titanium or migration of lithium. Then, the symmetry between a domain without reversal of polarization and the other domain with a reversed polarization becomes worse, and this deteriorates the properties of the resonator.
In order solve this problem, the inventors proposed a layered ferroelectric device with reversed polarizations by using direct bonding of ferroelectric plates in Japanese Patent laid open Publication 7-206600/1995. In this process, polarization is reversed easily, and properties are not deteriorated. However, the publication describes only a bonding process, and it does not describe or suggest how to use the ferroelectric plate for fabricating a ferroelectric (piezoelectric) resonator.
Further, even if a cut angle which excites only thickness-extensional vibration mode is selected for lithium niobate and lithium tantalate, there is a problem to be solved. Resonance energy of first order or fundamental wave is not trapped between the electrodes, and the resonator uses third order resonance. The coupling coefficient becomes a ninth because the coupling coefficient of n-th order resonance becomes 1/n.sup.2 for a higher order resonance. Because the characteristic of the resonator is proportional to the coupling constant, the resonator using the third order harmonic wave has worse characteristics than the resonator using the fundamental wave. Further, vibrations not trapped near the fundamental wave couple with other vibrations to generate forced vibrations of fundamental wave. Then, an element design is needed to operate a resonator of third harmonic wave properly. Further, for a square or circular element of a resonator of a thickness shear mode, the thickness shear wave (main wave) having faster sound velocity is excited at about the same level as the thickness shear wave (unnecessary wave) having a slower sound velocity.
Even if the resonator has a rectangular shape which is longer in the displacement direction of main wave, there is a limit to suppress slower unnecessary waves. Further, if a strip resonator is fabricated in order to suppress spurious resonances, the resonator has a shape of a long and narrow bar, and finishing of an end size thereof has a large influence on the vibration characteristics. Even if the end size is formed precisely, Q is deteriorated or new spurious resonances are generated if the end size has a bad cutting shape. Especially if the size of the resonator becomes thin for high frequencies, the width thereof becomes narrow, and this makes fabrication difficult and the resonator weak.